An applicator assembly of this kind is known, inter alia, from French Patent Specification No. 2 603 780, which describes a bottle comprising a neck, the opening of which narrows towards the bottom of the bottle to end in a passage into which the end of an applicator brush penetrates in order to be impregnated with the cosmetic product. In the case of an eyeliner tip, i.e. a very fine tip, the passage has a very small diameter in which sufficient capillary action is produced that the bottle does not leak, even if it is turned upside down. In the case of a mascara product, the applicator necessarily has a larger diameter, so that the diameter of the passage is at least of the order of 2 to 3.5 mm. In this case, the bottle leaks if it is turned upside down as there is no longer any capillary action.